Scanning Electron Microscopy and X-Ray Microanalysis

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19

the X-ray lines used for analysis.. Table 19.4 shows the

variation of the path length that can occur if one varies the

initial electron beam energy for Al K-L 3 X-rays in Al from

10 to 30 keV and the take-off angle, ψ = 15° and ψ = 60°.

The variation in PL is larger than a factor of 20, from

0.35 μm at the lowest keV and highest take-off angle to

7.7 μm at the highest keV and lowest take-off angle. Clearly

the analyst’s choices of the initial electron beam energy and

the X-ray take-off angle have a major effect on the path length

and therefore the amount of absorption that occurs.

In summary, using appropriate formulations for X-ray

generation with depth or φ(ρz) curves, the effect of absorp-

tion can be obtained by considering absorption of X-rays

from element i as they leave the sample. The absorption cor-

rection, Ai, can be calculated by taking the ratio of the effect of

absorption for the standard, Ai,std, to X-ray absorption for the

unknown, Ai,unk, for each element, i, in the sample. The effect

of absorption can be minimized by decreasing the path length

of the X-rays in the specimen through careful choice of the

initial beam energy and by selecting, when possible, a high

take-off angle.

X-ray Fluorescence, F

Photoelectric absorption results in the ionization of inner

atomic shells, and those ionizations can also cause the emis-

sion of characteristic X-rays. For fluorescence to occur, an

atom species must be present in the target which has a critical

excitation energy less than the energy of the characteristic

X-rays being absorbed. In such a case, the measured X-ray

intensity from this second element will include both the

direct electron-excited intensity as well as the additional

intensity generated by the fluorescence effect. Generally, the

fluorescence effect can be ignored unless the photon energy is

less than 5 keV greater than the critical excitation energy, Ec.

The significance of the fluorescence correction, Fi, can be

illustrated by considering the binary system Fe-Ni. In this sys-

tem, the Ni K-L 3 characteristic energy at 7.478  keV is greater

than the energy for excitation of Fe K radiation,

Ec = 7.11 keV. Therefore, an additional amount of Fe K-L 3 radi-

ation is produced beyond that due to the direct beam on Fe.

. Figure 19.5 shows the effect of fluorescence in the Fe-Ni sys-
tem at an initial electron beam energy of 30 keV and a take-off
angle, ψ, of 52.5°. Under these conditions, the atomic number
effect, ZFe, and the absorption effect, AFe, for Fe K-L 3 are very
close to 1.0. The measured kFe ratio lies well above the first
approximation straight line relationship. The additional inten-
sity is given by the effect of fluorescence. As an example, for a
10 wt% Fe – 90 wt% Ni alloy, the amount of iron fluorescence
is about 25 %.
The quantitative calculation of the fluorescence effect
requires a knowledge of the depth distribution over which the
characteristic X-rays are absorbed. The φ(ρz) curve of elec-
tron-generated X-rays is the starting point for the fluorescence
calculation, and a new φ(ρz) curve for X-ray- generated X-rays
is determined. The electron-generated X-rays are emitted iso-
tropically. From the X-ray intensity generated in each of the
layers Δ(ρz) of the φ(ρz) distribution, the calculation next
considers the propagation of that radiation over a spherical
volume centered on the depth ρz of that layer, calculating the
absorption based on the radial distance from the starting layer
and determining the contributions of absorption to each layer
(ρz) in the X-ray-induced φ(ρz) distribution. Because of the
longer range of X-rays than electrons in materials, the X-ray-
induced φ(ρz) distribution covers a much greater depth, gen-
erally an order of magnitude or more than the electron-induced
. Table 19.4 Path Length, PL, for Al K-L 3 X-rays in Al

E 0 Take-Off Angle, ψ Rx (μm) Path Length, PL,

(μm)

10 15 0.3 1.16

10 60 0.3 0.35

30 15 2.0 7.7

30 60 2.0 2.3

Eo

EDS

Detector

PL = Z COSEC Ψ

Specimen

PL = t

Ψ

Z

. Fig. 19.15 Schematic diagram showing the X-ray absorption path
length in a thick, flat-polished sample: PL = absorption path length;
ψ = X-ray take-off angle (detector elevation angle above surface)

Chapter 19 · Quantitative Analysis: From k-ratio to Composition